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Four positive integers p, q, r, s satisfy the following equations:

\(\begin{align*} pq+2p+q&=348 \\ qr+4q+3r&=373 \\ rs+8r+6s&=544 \end{align*}\)
What are p,q, r, and s?

 Mar 25, 2020
 #1
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Hint:

 

For this question, multiply one equation so that one variable can be subtracted!

 

For example, multiply pq+2+q by 2 so that it can be equal to the second equation.

 

Hope this helped!

 Mar 25, 2020
 #2
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p=1; q=1;r=1;s=1;p=1;m=0;n=p+q+r+s;if(n==348 and 373 and 544, goto8, goto next);m=(a*b+b*c+c*d);max(m)==p;print max(m);next:a++;if(a<55, goto5, 0);a=1;b++;if(b<55, goto5, 0);a=1;b=1;c++;if(c<55, goto5,0);a=1;b=1;c=1;d++;if(d<55, goto5, discard=0;

 

OUTPUT: r = 31 and s = 8 and p = 34 and q = 8

 Mar 25, 2020
 #3
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Can you please explain your work.

Guest Mar 25, 2020

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